{
  "id": "1805.01140",
  "version": "v1",
  "published": "2018-05-03T07:08:04.000Z",
  "updated": "2018-05-03T07:08:04.000Z",
  "title": "Weighted Least Squares Approximation by Orthogonal Polynomials with a Regularization Term",
  "authors": [
    "Congpei An",
    "Hao-Ning Wu"
  ],
  "comment": "13 pages, 5 figures (17 subfigures), version 1, revision needed",
  "categories": [
    "math.NA"
  ],
  "abstract": "In this paper we consider weighted least squares approximation by orthogonal polynomials with a regularization term on $[-1,1]$. The models are better than classical least squares even most regularized least squares due to their lead to closed-form solutions. The closed-form solution for models with $\\ell_2$-regularization term derive the closed-form expression of the Lebesgue constant for such an approximation. Moreover, we give bounds for the number of nonzero elements of the solution for models with $\\ell_1$-regularization term, which shows the sparsity of the solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-03T07:08:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65D10",
      "65D32",
      "94A99"
    ],
    "keywords": [
      "orthogonal polynomials",
      "squares approximation",
      "closed-form solution",
      "lebesgue constant",
      "closed-form expression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}